Statements 
Reasons 
1) AB = AC 
1) Given 
2) BD = CD 
2) Given 
3) AD = AD 
3) Reflexive (common side) 
4) ΔABD ≅ ΔACD 
4) By SSS postulate 
5) ∠BAP = ∠CAP 
5) By CPCTC ∠BAD = ∠CAD 
6) AP = AP 
6) Reflexive(common side) 
7) ΔBAP ≅ ΔCAP 
7) By SAS postulate 
8) ∠APB = ∠APC 
8) CPCTC 
9) BP = CP 
9) CPCTC 
10) ∠APB + ∠APC = 180 
10) These two angles are linear pair angles and they are supplementary 
11) 2∠APB = 180 
11) Addition property 
12) ang;APB = 90^{0}

12) Division property 
13) AP is the perpendicular bisector of BC 
13) By definition of perpendicular bisector and from (9) and (12) 